The people at Folktrax identify Mr. Wright's "Tally-I-O" with the shanty "Tiddy-I-O" found in Sharp and in Hugill (in different forms). Here is the Folktrax link (scroll down):

http://folktrax-archive.org/menus/search%20for%20titles_ti.htm

Here is Sharp's version from ENGLISH FOLK-CHANTEYS p. 46:

http://www.archive.org/stream/englishfolkchant00shar#page/46/mode/2up

And Hugill's version can be found on page 452 of the 1961 edition of SHANTIES FROM THE SEVEN SEAS.

All of this has been discussed at some length over in the "Rare Caribbean shanties" thread, particularly here (the posts in that thread seemed to be in reverse order):

thread.cfm?threadid=119776&messages=75&page=1&desc=yes#2675765

It's not clear that any of these three possibilities, from Mr.Wright (Carpenter), Mr. Rapsey (Sharp) or Mr. Smith (Hugill) is the shanty mentioned by Dana.